Boundary Conditions¶
Every step specifies what happens at each end of the column through two boundary conditions — one at the Top (\(z = L\)) and one at the Bottom (\(z = 0\)). The boundary condition determines whether gas enters, leaves, or is sealed at that face, and with what driving force.
Every step has a Top and a Bottom boundary. The first choice for each is its boundary condition type.
Boundary condition types¶
Pressure¶
Imposes a specified pressure at the face. Use it for steps controlled by a pressure level — pressurisation, blowdown, or a constant-pressure product outlet.
- As an inlet, you also specify the inlet Temperature and Composition; gas enters at the imposed pressure.
- As an outlet, the temperature and composition are taken from the bed (zero-gradient); gas leaves at the imposed pressure.
The pressure follows a Pressure Profile over the step (see Profiles below), so you can ramp the pressure up or down during the step. A pump (compressor or vacuum pump) can be attached to compute compression power and heating — see Pumps.
Flow¶
Imposes a molar flow at the face, specified through one or more streams. Use it for feed steps and for flow-controlled purge or product steps.
A Flow boundary contains a list of streams (add them with Add Stream); the total flow is the sum of the streams. Each stream has:
- a Boundary Device Type — None (flow specified directly), Valve (pressure-driven), or Pump (power-driven);
- for a None device, a Flow Type and a flow profile;
- as an inlet, its own Temperature and Composition.
Multiple streams on one face let you, for example, mix a fresh feed with a recycle stream.
Closed¶
A sealed, no-flow end. Nothing enters or leaves; pressure, temperature and composition have zero gradient at the face. Use it for the closed end of a blowdown or equalisation step. A Closed boundary has no further settings.
Flow direction¶
Each boundary has a Flow direction:
- Inlet — gas flows into the reactor. You specify what enters (temperature, composition, and — for a Flow boundary — the flow rate).
- Outlet — gas flows out of the reactor. The leaving gas takes the bed's local temperature and composition.
A step must have at least one non-inlet end (an outlet or a closed end); the two ends cannot both be inlets.
Specifying inlet flow¶
For a Flow boundary with a None device, the Flow Type sets how the rate is expressed. All four are equivalent and are converted internally using the boundary-face area and the ideal-gas density:
| Flow Type | Quantity |
|---|---|
| Velocity | Superficial velocity [m s⁻¹] |
| Volumetric Flow Rate | Volumetric flow [m³ s⁻¹] |
| Molar Flow Rate | Molar flow [mol s⁻¹] |
| Mass Flow Rate | Mass flow [kg s⁻¹] |
Inlet composition and temperature¶
At an inlet you set the Temperature and the Composition (a mole fraction for each component). The mole fractions of an inlet must sum to 1. Outlets ignore these fields because the leaving gas is whatever is in the bed.
Inlet temperature profile¶
The inlet temperature of a stream (or of a Pressure inlet) can change during the step, for example to ramp a TSA feed or regeneration gas from cold to hot without splitting the step. Pick a Temperature Profile:
- Constant — the default: the single Temperature above, held for the whole step. Decks saved before temperature profiles existed load as Constant and are unchanged.
- Linear — from the Start Temperature \(T_0\) to the Final Temperature \(T_1\) over the Ramp Time \(t_r\), then held at \(T_1\) (it never extrapolates past the end of the ramp):
- Exponential — a first-order approach from \(T_0\) to \(T_1\) whose remaining change has shrunk by the Exponential Factor \(F\) after the ramp time \(t_r\) (the default \(F = 100\) has covered 99 % of the change by then):
- Log-linear — a geometric ramp from \(T_0\) to \(T_1\) over the ramp time, then held at \(T_1\) (see time-varying profiles).
\(t\) is the time since the start of the step, so the ramp restarts every time the step runs. A ramp time of zero is an immediate step to \(T_1\), and a ramp longer than the step simply ends part-way. Switching from Constant starts both temperatures at the current value with a ramp time equal to the step time.
The profile replaces the typed-in temperature only. When the inlet is fed from a buffer tank or a connected stream, the gas keeps that source's temperature as before, and the profile acts as the first-cycle assumption. In an isothermal run inlet temperatures have no effect.
Heating and cooling the column¶
A step can also heat or cool the column from outside, through a heating medium on the wall's outer face: a jacket fluid at a set temperature (constant or ramped, with the same profiles as an inlet temperature) and heat transfer coefficient. It replaces the ambient exchange while the step runs; steps without one keep it.
Time-varying profiles¶
Flow rates, pressures and inlet temperatures can all vary during a step. The Profile Type (for flow) or Pressure-Time Profile (for pressure) offers:
- Constant — a single value held for the whole step.
- Linear — ramps linearly from a Start Value to a Final Value over a Ramp Time.
- Exponential — approaches the Final Value \(v_1\) from the Start Value \(v_0\) with a first-order response: after the ramp time \(t_r\) the change left is \(1/F\) of the initial one, where \(F\) is the Exponential Factor (default 100, i.e. 99 % of the change covered by \(t_r\); it must be greater than 1). The curve keeps approaching \(v_1\) after \(t_r\):
- Log-linear — a geometric ramp from the Start Value \(v_0\) to the Final Value \(v_1\) over the ramp time \(t_r\), then held at \(v_1\). The value is multiplied by the same factor every second, so \(\ln v\) rises linearly:
Ramps are the natural way to model gradual pressurisation or blowdown.
Pressure ramps (a Pressure boundary or a valve) start from the bed pressure at the start of the step, so they have no Start Value. By default (Use Step Time on) the ramp lasts the whole step. Turn it off to give the ramp its own Ramp Time, for example to pressurise in the first 10 s of a 30 s step and hold the final pressure for the rest; the ramp time must be no longer than the step (the run is refused otherwise). Decks saved before this option existed ramp over the step time, as before.
Choosing a pressurisation ramp¶
In upward flow the pressure gradient at the bed inlet scales roughly with \(d\ln P/dt\), the boundary pressure's rate of rise relative to the pressure itself (in the viscous regime \(-\partial P/\partial z \propto \mu R T N / (K P)\), and the molar flux \(N\) needed to fill the bed scales with \(dP/dt\)). A linear ramp from vacuum has its largest relative rise in the first seconds: from 3 kPa to 4.6 bar in 20 s it starts at 7.6 s⁻¹ and ends at 0.05 s⁻¹, which is where a spike in the approach to fluidisation appears. An exponential ramp front-loads the rise even more (35 s⁻¹ at the start). A log-linear ramp holds \(d\ln P/dt\) at \(\ln(P_1/P_0)/t_r\) (0.25 s⁻¹ here) for the whole step, so the gradient is spread evenly. The trade-off is that the bed stays at low pressure for longer (only \(\sqrt{P_0 P_1}\) halfway through) and the pressure rises fastest in absolute terms at the end of the step, so check the approach to fluidisation there too, and the cycle's performance.
A geometric ramp cannot start from or pass through zero, so when the start or final value is zero or negative the log-linear profile ramps linearly instead (for example a flow ramp that starts from zero).
- Double exponential — a two-term decay towards the Final Value: a share \(w\) of the initial excess decays at Rate 1 and the rest at Rate 2 (both in s⁻¹, entered as fitted, not as a 99 % time):
This is the form Estupiñan Perez et al. (2019) fitted to the evacuation pressure of their VSA rig (a fast term for the column gas, a slow one for the pump and piping, \(r_1 = 0.019\) and \(r_2 = 0.101\) s⁻¹), where a single exponential did not describe the measured curve. For a pressure the start is the bed pressure at the start of the step; a rate of zero freezes its term at the start value.
All numeric fields accept expressions and units, e.g.
2 [bar]or a reference to a global variable.
Valves¶
Set a stream's Boundary Device Type to Valve to make its flow pressure-driven rather than prescribed. You enter a Valve Flow Coefficient (Cv) and a pressure profile; the flow through the valve is driven by the pressure difference between the valve's set pressure and the bed. The valve is linear in the pressure difference (Valve::GetMolarFlowRate in core/src/objects/valve.cpp):
so \(C_v\) is in mol s⁻¹ bar⁻¹: a valve with \(C_v = 10\) passes 10 mol/s for a 1 bar difference. Gas flows from the higher to the lower pressure, and the flow reverses if the pressures cross.
The bed side of the law is the pressure at the bed end (the boundary face, the mean of the ghost cell and the end cell). The solver setting settings.valve_bed_pressure ("Valve_Bed_Pressure" in Solver_Settings; IDASettings::valve_bed_pressure_) can instead read the pressure of the end cell, the last cell at that end of the bed, as models that treat the column as a series of well-mixed cells do (toPSAil attaches its valves to the last cell). A connected valve then reads its partner's end cell as well. The two readings differ by the pressure drop over half a cell and agree as the grid is refined; use end_cell only to compare with such a model.
Valves are the mechanism behind pressure equalisation: put a valve on each bed and connect them, and gas flows from the high-pressure bed to the low-pressure one at a rate set by Cv.
Pumps: compressors and vacuum pumps¶
A Pump device (or a pump attached to a Pressure boundary) models mechanical compression:
- an inlet uses a compressor (with a Suction Pressure);
- an outlet uses a vacuum pump (with a Discharge Pressure).
The pump settings include an Efficiency Model (constant Isentropic Efficiency, a vacuum-pump curve, or a polynomial), a Polytropic Constant, and an Energy Model (Isothermal or Adiabatic) that determines the outlet-gas temperature rise from compression. The efficiency is evaluated at the pump's suction pressure \(P_1\) (in Pa); the polynomial is the full fifth-degree one:
There are two distinct uses:
- Power-controlled flow — a Pump device on a Flow stream sets the molar flow from a specified power (constant or a polynomial in pressure). This affects the simulation.
- Power for post-processing — ticking Calculate pump power on a Pressure boundary or a None stream computes compression power and heating for reporting, without changing the flow the boundary imposes. The recorded power feeds the energy-consumption KPI.
Drawing gas from another step (buffer tank)¶
An inlet can be fed from the gas produced by another step instead of from values you type in. Tick Use buffer tank from another step under Inlet Source, choose the source step and endpoint, and set the percentage of that step's produced moles to draw. This is the basis of averaged light reflux and recycle.
Next, learn how to couple two beds together in Connecting Beds.